Which of the following events are equal? (a) A={1,3}; (b) B={x |x is a number on a die } : (c) C

step 1 Hi, here in the question we have to find which of the following events are equal. Okay, the firs

Which of the following events are equal? (a) A={1,3}; (b)...

Which of the following events are equal?
(a) $A=\{1,3\}$;
(b) $B=\{x \mid x$ is a number on a die $\}$ :
(c) $C=\left\{x \mid x^{2}-4 x+3=0\right\}$
(d) $D=\{x \mid \mathrm{x}$ is the number of heads when six coins are tossed $\}$

Key Concepts

Set Equality

Set equality is the principle that two sets are equal if and only if they contain exactly the same elements, regardless of the order in which they are listed or how they are described. This concept is essential when comparing different ways of specifying events or outcomes in probability and mathematics.

Solving Quadratic Equations

Solving quadratic equations involves finding the values of the variable that satisfy the equation. In particular, by factoring or applying the quadratic formula, one can determine the roots of an equation, which can then be interpreted as a set of solutions. Understanding this process is important when an event is defined by a quadratic equation.

Sample Spaces in Probability

A sample space is the set of all possible outcomes of a probabilistic experiment. For example, rolling a die or tossing coins generates different sample spaces, which form the basis for defining events. Recognizing the sample space is crucial for interpreting and comparing events in probability theory.

Event Definition in Probability

Events in probability are defined as specific subsets of a sample space. An event can be described explicitly by listing its outcomes or implicitly by stating the conditions that the outcomes must satisfy. This concept is key to understanding and comparing different events in terms of their constituent outcomes.

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